Comparing Anti-foundation Axioms by Comparing Identity Conditions for Sets

2024/12/08 by Daheng Ju, Ju, Daheng, Qihang Jing +1 · 1 citation
Computer Science · #Constraint Satisfaction and Optimization #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2412.05914

openalex publication_date 2024/12/08 · openalex created_date 2024/12/12 · openalex updated_date 2026/07/28

Abstract

In non-well-founded set theory, which anti-foundation axiom is philosophically justified, BAFA, FAFA, SAFA, AFA, or some other? In this paper, we investigate a general approach to answering this question: first, consider which identity condition for sets is justified; second, consider which anti-foundation axiom it justifies. Specifically, we study in detail two plausible identity conditions.

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